A method of cleaning a filtration membrane includes an alkaline treatment process for supplying an alkaline agent (24) to seawater (11) for a predetermined period of time and filtering the seawater (11), to which the alkaline agent (24) is supplied, through a reverse osmosis membrane (15) during a filtration treatment operation, and a neutralization treatment process for supplying an acid agent (26) to the seawater (11) for a predetermined period of time and filtering the seawater (11), to which the acid agent (26) is supplied, through the reverse osmosis membrane (15) after the alkaline treatment process.